Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A researcher collects data on the number of cars passing through an intersection each hour. What type of variable is this?

Accepted Answer

Quantitative and discrete, because the values are countable.

Question 3

Which of the following is the correct formula for the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{\sum x_i}{n}$$

Question 4

A physical therapist records the body part requiring rehabilitation for 30 patients. Which graphical display is most appropriate for summarizing this qualitative data?

Accepted Answer

Bar graph

Question 5

Given the following frequency table for body parts requiring rehabilitation, what is the relative frequency for 'Knee' if there are 5 cases out of 30?

Accepted Answer

$$\frac{5}{30} = 0.167$$

Question 6

Which of the following statements about the Empirical Rule is correct for a bell-shaped distribution?

Accepted Answer

Approximately 95% of the data lie within 2 standard deviations of the mean.

Question 7

A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 60?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 8

Which of the following is the correct formula for the sample variance $$s^2$$?

Accepted Answer

$$s^2$$ = \frac{\sum (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 9

A researcher wants to compare the heights of plants grown with two different fertilizers. Which statistical test should be used?

Accepted Answer

Two-sample t-test for independent samples

Question 10

Suppose the probability of a randomly selected person being left-handed is 0.1. In a group of 5 people, what is the probability that exactly 2 are left-handed? (Use the binomial formula.)

Accepted Answer

$$P(X=2) = \binom{5}{2} (0.1)^2$ (0.9)^3$

Question 11

Which of the following is NOT a requirement for using the one-way ANOVA test?

Accepted Answer

The sample sizes must be equal.

Question 12

A 95% confidence interval for a population mean is calculated as (12.5, 17.5). What is the correct interpretation?

Accepted Answer

We are 95% confident that the population mean is between 12.5 and 17.5.

Question 13

Which of the following is the correct formula for the test statistic in a one-sample t-test?

Accepted Answer

$$t = \frac{\bar{x} - \mu_0$}{s/\sqrt{n}}$$

Question 14

A chi-square goodness-of-fit test is used to:

Accepted Answer

Test whether observed frequencies match expected frequencies for a categorical variable.

Question 15

Which of the following is a correct interpretation of a p-value in hypothesis testing?

Accepted Answer

The probability of obtaining a result as extreme or more extreme than the observed, assuming the null hypothesis is true.

Question 16

If a distribution is skewed right, which measure of center is most appropriate to report?

Accepted Answer

Median, because it is resistant to extreme values.

Question 17

Which of the following is the formula for the confidence interval for a population proportion $$p$$?

Accepted Answer

$$\hat{p} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 18

A researcher wants to know if a new medication changes the average recovery time for a disease. Which is the appropriate null hypothesis?

Accepted Answer

$$H_0$$: \mu = \$$mu_0$$

Question 19

Which of the following is the correct formula for the standard error of the mean when sampling from a population with standard deviation $$\sigma$$ and sample size $$n$$?

Accepted Answer

$$\frac{\sigma}{\sqrt{n}}$$

Introductory Statistics Formula Sheet and Reference Tables

Study Guide - Practice Questions

Study Guide - Flashcards